
Re: matrix analysis: can I say matrix X=Y if I have AXA=AYA?
Posted:
Mar 10, 2004 3:38 PM


1. the dimensions of A,X,Y should be compatible, in this case I think they should be all square matrices.
2. If you require that AXA=AYA for all matrices A, then it would certainly hold for A=identity matrix.
3. If A is some unknown matrix, i.e. then AXA=AYA tells you not much. E.g. if A=[0]
Joenyim Kim wrote: > Dear all, > > I wonder under what condition can I say X=Y if I have AXA=AYA? > > A is any matrix, not neccessarily square or nonsingular... it can be > rectangular and singular... > > Then can AXA=AYA reduce to X=Y? > >  > > I myself conceived that > > I can write AXA=AYA to be A(XY)A=0, since A is arbitarily any matrix, the > only possible case is X=Y, > > am I right? > > Thanks a lot, > > Joenyim > >
 Best regards, Alex.
PS. To email me, remove "loeschedies" from the email address given.

